A stochastic population projection system based on general age-dependent branching processes

"Algorithms for a stochastic population process, based on assumptions underlying general age-dependent branching processes in discrete time with time inhomogeneous laws of evolution, are developed through the use of a new representation of basic random functions involving birth cohorts and random sums of random variables. New algorithms provide a capability for computing the mean age structure of the process as well as variances and covariances, measuring variation about means. Four exploratory population projections, testing the implications of the algorithms for the case of time-homogeneous laws of evolution, are presented. Formulas extending mean and variance functions for unit population projections...are also presented. These formulas show that, in population processes with non-random laws of evolution, stochastic fluctuations about the mean function are negligible when initial population size is large. Further extensions of these formulas to the case of randomized laws of evolution suggest that stochastic fluctuations about the mean function can be significant even for large initial populations."     

The first three anisotropy constants of nickel

The technique of ferromagnetic resonance at 23 GHz has been used to determine the first three anisotropy constants of pure Ni down to 4.2K. A temperature and orientation dependent linewidth has also been observed.     

Manifold preprocessing for laser‐induced breakdown spectroscopy under Mars conditions

Laser‐induced breakdown spectroscopy (LIBS) is currently being used onboard the Mars Science Laboratory rover Curiosity to predict elemental abundances in dust, rocks, and soils using a partial least squares regression model developed by the ChemCam team. Accuracy of that model is constrained by the number of samples needed in the calibration, which grows exponentially with the dimensionality of the data, a phenomenon known as the curse of dimensionality. LIBS data are very high dimensional, and the number of ground‐truth samples (i.e., standards) recorded with the ChemCam before departing for Mars was small compared with the dimensionality, so strategies to optimize prediction accuracy are needed. In this study, we first use an existing machine learning algorithm, locally linear embedding (LLE), to combat the curse of dimensionality by embedding the data into a low‐dimensional manifold subspace before regressing. LLE constructs its embedding by maintaining local neighborhood distances and discarding large global geodesic distances between samples, in an attempt to preserve the underlying geometric structure of the data. We also introduce a novel supervised version, LLE for regression (LLER), which takes into account the known chemical composition of the training data when embedding. LLER is shown to outperform traditional LLE when predicting most major elements. We show the effectiveness of both algorithms using three different LIBS datasets recorded under Mars‐like conditions. Copyright © 2015 John Wiley & Sons, Ltd.